There’s a lot of discussion about ADC resolution and SDRs. I’m trying to develop a simple HF data system that uses RTL-SDRs in “Direct Sample” mode. This blog post describes how I measured the Minimum Detectable Signal (MDS) of my 100 bit/s 2FSK receiver, and a spreadsheet model of the receiver that explains my results.
Noise in a receiver comes from all sorts of places. There are two sources of concern for this project – HF band noise and ADC quantisation noise. On lower HF frequencies (7MHz and below) I’m guess-timating signals weaker than -100dBm will be swamped by HF band noise. So I’d like a receiver that has a MDS anywhere under that. The big question is, can we build such a receiver using a low cost SDR?
Experimental Set Up
So I hooked up the experimental setup in the figure below:
The photo shows the actual hardware. It was spaced apart a bit further for the actual test:
Rpitx is sending 2FSK at 100 bit/s and about 14dBm Tx power. It then gets attenuated by some fixed and variable attenuators to beneath -100dBm. I fed the signal into a RTL-SDR plugged into my laptop, demodulated the 2FSK signal, and measured the Bit Error Rate (BER).
I tried a command line receiver:
rtl_sdr -s 1200000 -f 7000000 -D 2 - | csdr convert_u8_f | csdr shift_addition_cc `python -c "print float(7000000-7177000)/1200000"` | csdr fir_decimate_cc 25 0.05 HAMMING | csdr bandpass_fir_fft_cc 0 0.1 0.05 | csdr realpart_cf | csdr convert_f_s16 | ~/codec2-dev/build_linux/src/fsk_demod 2 48000 100 - - | ~/codec2-dev/build_linux/src/fsk_put_test_bits -
and also gqrx, using this configuration:
with the very handy UDP output option sending samples to the FSK demodulator:
$ nc -ul 7355 | ./fsk_demod 2 48000 100 - - | ./fsk_put_test_bits -
Both versions demodulate the FSK signal and print the bit error rate in real time. I really love the csdr tools, and gqrx is also great for a more visual look at the signal and the ability to monitor the audio.
For these tests the gqrx receiver worked best. It attenuated nearby interferers better (i.e. better sideband rejection) and worked at lower Rx signal levels. It also has a “hardware AGC” option that I haven’t worked out how to enable in the command line tools. However for my target use case I’ll eventually need a command line version, so I’ll have to improve the command line version some time.
The RF Gods are smiling on me today. This experimental set up actually works better than previous bench tests where we needed to put the Tx in another room to get enough isolation. I can still get 10dB steps from the attenuator at -120dBm (ish) with the Tx a few feet from the Rx. It might be the ferrites on the cable to the switched attenuator.
I tested the ability to get solid 10dB steps using a CW (continuous sine wave) signal using the “test” utility in rpitx. FSK bounces about too much, especially with the narrow spec an settings I need to measure weak signals. The configuration of the Rigol DSA815 I used to see the weak signals is described at the end of this post on the SM2000.
The switched attenuator just has 10dB steps. I am getting zero bit errors at -115dBm, and the modem fell over on the next step (-125dBm). So the MDS is somewhere in between.
This spreadsheet (click for the file) models the receiver:
By poking the RTL-SDR with my signal generator, and plotting the output waveforms, I worked out that it clips at around -30dBm (a respectable S9+40dB). So that’s the strongest signal it can handle, at least using the rtl_sdr command line options I can find. Even though it’s an 8 bit ADC I figure there are 7 magnitude bits (the samples are unsigned chars). So we get 6dB per bit or 42dB dynamic range.
This lets us work out the the power of the quantisation noise (42dB beneath -30dBm). This noise power is effectively spread across the entire bandwidth of the ADC, a little bit of noise power for each Hz of bandwidth. The bandwidth is set by the sample rate of the RTL-SDRs internal ADC (28.8 MHz). So now we can work out No (N-nought), the power/unit Hz of bandwidth. It’s like a normalised version of the receiver “noise floor”. An ADC with more bits would have less quantisation noise.
There follows some modem working which gives us an estimate of the MDS for the modem. The MDS of -117.6dBm is between my two measurements above, so we have a good agreement between this model and the experimental results. Cool!
Falling through the Noise Floor
The “noise floor” depends on what you are trying to receive. If you are listening to wide 10kHz wide AM signal, you will be slurping up 10kHz of noise, and get a noise power of:
-146.6+10*log10(10000) = -106.6 dBm
So if you want that AM signal to have a SNR of 20dB, you need a received signal level of -86.6dB to get over the quantisation noise of the receiver.
I’m trying to receive low bit rate FSK which can handle a lot more noise before it falls over, as indicated in the spreadsheet above. So it’s more robust to the quantisation noise and we can have a much lower MDS.
The “noise floor” is not some impenetrable barrier. It’s just a convention, and needs to be considered relative to the bandwidth and type of the signal you want to receive.
One area I get confused about is noise bandwidth. In the model above I assume the noise band width is the same as the ADC sample rate. Please feel free to correct me if that assumption is wrong! With IQ signals we have to consider negative frequencies, complex to real conversions, which all affects noise power. I muddle through this when I play with modems but if anyone has a straight forward explanation of the noise bandwidth I’d love to hear it!
At the suggestion of Mark, I repeated the MDS tests with a strong CW interferer from my signal generator. I adjusted the Sig Gen and Rx levels until I could just detect the FSK signal. Here are the results, all in dBm:
|Sig Gen||2FSK Rx MDS||Difference|
The FSK signal was at 7.177MHz. I tried the interferer at 7MHz (177 kHz away) and 7.170MHz (just 7 kHz away) with the same blocking results. I’m pretty impressed that the system can continue to work with a 65dB stronger signal just 7kHz away.
So the interferer desensitises the receiver somewhat. When listening to the signal on gqrx, I can hear the FSK signal get much weaker when I switch the Sig Gen on. However it often keeps demodulating just fine – FSK is not sensitive to amplitude.
I can also hear spurious tones appearing; the quantisation noise isn’t really white noise any more when a strong signal is present. Makes me feel like I still have a lot to learn about this SDR caper, especially direct sampling receivers!
As with the MDS results – my blocking results are likely to depend on the nature of the signal I am trying to receive. For example a SSB signal or higher data rate might have different blocking results.
Still, 65dB rejection on a $27 radio (at least for my test modem signal) is not too shabby. I can get away with a S9+40dB (-30dBm) interferer just 7kHz away with my rx signal near the limits of where I want to detect (-96dBm).
So I figure for the lower HF bands this receivers performance is OK – the ADC quantisation noise isn’t likely to impact performance and the strong signal performance is good enough. An overload of -30dBm (S9+40dB) is also acceptable given the use case is remote communications where there is unlikely to be any nearby transmitters in the input filter passband.
The 100 bit/s signal is just a starting point. I can use that as a reference to help me understand how different modems and bit rates will perform. For example I can increase the bit rate to say 1000 bit/s 2FSK, increasing the MDS by 10dB, and still be well beneath my -100dBm MDS target. Good.
If it does falls over in the real world due to MDS performance, overload or blocking, I now have a good understanding of how it works so it will be possible to engineer a solution.
For example a pre-amp with X dB gain would lower the quantisation noise power by X dB and allow us to detect weaker signals but then the Rx would overload at -30-X dB. If we have strong signal problems but our target signal is also pretty strong we can insert an attenuator. If we drop in another SDR I can recompute the quantisation noise from it’s specs, and estimate how well it will perform.